Chapter 12.6, Problem 12E

In Problems 5 -12 , either by hand or using computer software package, sketch the phase plane diagram for the given system. Discuss the stability of each limit cycle and critical point. Here $x=r\cos \theta$ and $y=r\sin \theta$.

$\frac{dx}{dt}=y+\frac{x}{r}\sin \left(r\right)$, $\frac{dx}{dt}=-x+\frac{y}{r}\sin \left(r\right)$